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4-01 - 4-1 Determine the mass density for the mixing...

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4-1. Determine the mass density, ρ , for the mixing process illustrated in Figure 4-1. 4-1. The mixing process illustrated in Figure 4-1 is a batch process in which the mass of each species is conserved. We express this idea as o o o , , A A A B B B C C V V V V V ρ = ρ ρ = ρ ρ = ρ C V o 3 (1) and we can solve for the three species densities in the final mixture to obtain (2) o o / , / , / A A A B B B C C C V V V V V V ρ = ρ ρ = ρ ρ = ρ The numerical results are given by (3) 3 3 0.283 g/cm , 0.317 g/cm , 0.356 g/cm A B C ρ = ρ = ρ = This type of calculation is intuitively obvious; however, it is worthwhile to understand the framework of the calculation in terms of the concepts presented in Chapter 4. The macroscopic mass balance for species A can be expressed as ( ) ( ) ( ) ( ) A A A t t t d dV dA r dV dt ρ + ρ = v w n V A V A (4) where V represents a control volume that properly represents the mixing process during which species B and C are added to species A . Since there is no chemical reaction
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